GMAT Data Sufficiency - If x and y are Positive Integers and xy is Divisible by Prime Number. Is p an Even Number?

Question: If x and y are positive integers and xy is divisible by prime number. Is p an even number?

1. \(x^2*y^2\)is an even number
2. xp = 6

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“If x and y are positive integers and xy is divisible by prime number. Is p an even number?” – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Answer:

Approach Solution 1

Notice that as given as given that p s a prime number and only even prime is 2, then the question basically asks whether p = 2.

(1) \(x^2*y^2\) is an even number. \(x^2*y^2\) = even means that xy = even. We have that some even number is divisible by prime number p, not sufficient to say whether p = 2, for example if xy = 6 then p can either be 2 or 3.

(2) xp = 6. Since x is a positive integer and p is a prime number then either x = 2 and p = 3 (answer NO) or x = 3 and p = 2 (answer YES). Hence, NOT SUFFICIENT.

(1) + (2) If y = 6 then xy = even so the first statement is satisfied irrespective of the value of x and thus we have no constraints on its value. So from (2) x can take any of the two values 2 or 3, which means that p can also take any of the two values 2 or 3, respectively.

Hence, NOT SUFFICIENT.

Correct option: E

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